Related papers: Decomposing the Spectral Form Factor
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite $N$ with non-zero inverse temperature. Using this…
The physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
Spectral functions are central to link experimental probes to theoretical models in condensed matter physics. However, performing exact numerical calculations for interacting quantum matter has remained a key challenge especially beyond one…
We derive expressions for strangeness-changing scalar form factors, which incorporate known theoretical constraints both at low and high energies. Their leading behaviour in the limit of a large number of colours is calculated from the…
In this work, the dynamics of dephasing (without relaxation) in the presence of a chaotic oscillator is theoretically investigated. The time-dependent density functional theory (TDDFT) framework was employed in tandem with the Lindblad…
Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model…
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…
In this work, we investigate the quantum chaos in various $T\bar{T}$-deformed SYK models with finite $N$, including the SYK$_4$, the supersymmetric SYK$_4$, and the SYK$_2$ models. We numerically study the evolution of the spectral form…
With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
Point processes have broad applications in science and engineering. In physics, their use ranges from quantum chaos to statistical mechanics of many-particle systems. We introduce a spatial form factor (SFF) for the characterization of…
Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…
Many-body systems undergoing quantum phase transitions reveal substantial growth of non-classical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy.…
The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the…